2024. Cristofer Caballeros: Advisor: Anthony Johnson

2024. Lauren Kimpel: Some Fellow-Traveler Properties on Finite Graphs Advisor: Nandi Leslie
This thesis investigates an application of the k-fellow-traveler property for groups to finite graphs (which may or may not be Cayley), and what may be possibly revealed about the structure of the graph by analyzing its k-fellow-traveler constant. We prove that, if G is a finite graph with κ(G) ≥ 2, then diam(G) − 1 ≤ kG ≤ diam(G).

2024. Donald Grage: Optimization of Rocket and Signature Techniques Using Synthetic Patient Data to Predict Type 2 Diabetes Advisor: Thomas Woolf
This thesis explores the application of Time Series Classification (TSC) methods, specifically ROCKET and Signature Method, for predicting Type 2 Diabetes from synthetic patient data. The project attempts to enhance the predictability of Diabetes diagnoses by analyzing medical observation data through advanced mathematical and programming techniques.

2024. Victoria Rose: Graphical Analysis of Recurrent Surface Temperature Trends Using the Gromov-Wasserstein Distance Metric Advisor: Thomas Woolf
Graphical networks serve as powerful models for interpreting complex systems by abstracting complex scenarios with a simple network. This work leverages such networks to model the patterns in surface temperature observed within the Gulf of Mexico. To quantify seasonal dynamics, Voronoi diagrams are used to capture sub-regions that share common characteristics. Graphs of these diagrams can then be analyzed like graphs and the Gromov-Wasserstein distance metric captures in a single metric how different a daily graph is from some standard reference graph.

2023. Jonah Bregstone: Modeling Pollinator Behavior Through Survival Analysis. Advisor: Thomas Woolf
This study applies survival analysis to pollinator-plant relationships, modeling floral-resource utilization by pollinators. Three types of survival analysis models are compared, including the Cox proportional hazards model, a binary classification model using stacking, and a Logistic Hazards neural network model.

2023. Frederick Day-Lewis: Advisor: David Schug

2023. Sarah Miller: Advisor: Cetin Savkli

2023. Ernest Friedel: Advisor: Kurt Stein

2023. Tulio Tablada: Advisor: Cleon Davis

2023. Jack Moody: Advisor: Thomas Woolf

2023. Lanfranco Bonghi: Advisor: Christine Nickel

2022. Michael Baeder: Manifold Learning for Empirical Asset Pricing. Advisor: Burhan Sadiq
This thesis develops a methodology for applying modern manifold embedding algorithms to the problem of empirical asset pricing. Our technique combines traditional linear compression with geometric dimensionality reduction in order to characterize the time-evolving distribution of a nonconstant dimensional time series using a small number of latent factors.

2022. Alyssa Columbus: Sleep Duration as a Neural Survival Model. Advisor: Thomas Woolf
This thesis focuses on modeling sleep duration with the most prominent medical model for sleep, the two-process model, in conjunction with a novel mathematical architecture that aspires to capture both the circular nature and the complexity of daily schedules and habits. Specifically, the two aims of this thesis are (1) to develop a theoretical mathematical framework to describe cyclical sleep and wake patterns and (2) to test this framework computationally with empirical patient data.

2022. Joseph Avila: Advisor: Nandi Leslie

2022. Anjelika Klamp: Advisor: Thomas Woolf

2022. Timothy Davison: Advisor: David Schug

2021. Richard Shea. Building a Dynamic Hawkes Graph. Advisor: Thomas Woolf.
We couple a multivariate description with a time-dependent Hawkes/INAR(p) process. This model can be updated by sensors and is essentially a Kalman filter for INAR coupled data streams. This is a way to automatically interrogate an incoming stream of data for change-points and to adjust the stationary distribution to a new stationary distribution when/if the underlying stream of data is seen to have changed.

2021. William Glad: Path Signature Area-Based Causal Discover in Coupled Time Series. Advisor: Thomas Woolf.
There are many techniques available to recover causal relationships from data, such as Granger causality, convergent cross mapping, and causal graph structure learning approaches such as PCMCI. Path signatures and their associated signed areas provide a new way to approach the analysis of causally linked dynamical systems, particularly in informing a model-free, data-driven approach to algorithmic causal discovery. With this paper, we explore the use of path signatures in causal discovery and propose the application of confidence sequences to analyze the significance of the magnitude of the signed area between two variables.

2021. Lucas McCabe. Markov Decision Processes for Node Immunization. Advisor: Thomas Woolf.
In this work, we consider the challenge of node immunization where information regarding network topology is inferred only through agent exploration along an unbiased random walk. In the first part, we formulate this as a Markov decision process problem and derive heuristic-based policies for scale-free and uncorrelated networks. We demonstrate empirical evidence that these policies achieve their objectives near-optimally and provide a policy-of-policies for situations where information about network family does not exist. In the second part, we introduce our open-source contagion package and use it to illustrate immunization policy performance with contagion simulations.

2021. Adam Byerly. Enhanced Uniform Manifold Approximation and Projection via Simultaneous Perturbation Stochastic Approximation. Advisor: Stacy Hill.
This thesis introduces the UMAP-SPSA algorithm to perform the UMAP dimension reduction without the need for the smooth approximator. Further, we analyze the algorithm’s computational performance and embedding accuracy.

2021. James Howard: Predicting Sepsis Onset with Survival Analysis Over Signature Transformations Advisor: Thomas Woolf
Predicting clinical outcomes from time-series medical data is a complex but essential endeavor. In this study, we propose a novel approach that combines traditional survival models like Cox pro- portional hazards, logistic, and multi-task logistic regression (MTLR) with the robust mathematical framework of signature methods. These methods are particularly effective in capturing the under- lying dynamics of time-series data with stochastic error. We introduce the concept of rough paths to provide a foundational understanding of how these techniques can capture not only the data’s deterministic aspects but also its stochastic nature, thereby enriching the feature set used for making more accurate predictions.

2020. Erick Galinkin. Malicious Network Traffic Detection via Deep Learning: An Information Theoretic View. Advisor: Cleon Davis.
Our results show that since mutual information remains invariant under homeomorphism, only feature engineering methods that alter the entropy of the dataset will change the outcome of the neural network. This means that for some datasets and tasks, neural networks require meaningful, human-driven feature engineering or changes in architecture to provide enough information for the neural network to generate a sufficient statistic.

2019. Dominic Michael Padova. Batlas: variational reconstruction of a digital, three-dimensional atlas of the big brown bat (Eptesicus fuscus). Advisors: Cleon Davis and J. Tilak Ratnanather.
We define Sobolev and total variation priors on image smoothness, which control the derivatives of the images, to regularize (i.e. reduce complexity by removing unreasonable parameter choices from) the high-dimensional parameter space prescribed by the rigid motion dimensions and the diffeomorphism dimensions. We show that the quality of rigid slice alignment brought by introducing a Sobolev prior on the image intensity of a phantom and the bat brain data is superior to that of the total variation priors.